A $$400m$$ long horizontal pipe is to deliver $$900$$ kg of oil
$$\left( {S = 0.9,\,\,\upsilon = 0.0002{m^2}/s} \right)$$ per minute. If the head loss is not to exceed $$8$$ $$m$$ of oil, find the pipe diameter.

(Friction factor in laminar flow: $$f = 64/{R_e}$$)

The stream function in a two dimensional flow field is given by $$\Psi = {x^2} - {y^2}$$
The magnitude of the velocity at point $$(1,1)$$ is

Two black plates, each one meter square, are placed parallel to each other in such a way that the radiation shape factor for the system is $$0.4.$$ If the plates are maintained at $${800^ \circ }C$$ and $${400^ \circ }C$$ respectively, determine the net radiant heat transfer between the plates. Also calculate the net heat exchange if the plates were infinite in size. Stephen Boltzmann constant $$ = 5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$

The total efficiency, $${\eta _t}$$ for a finned surface may be defined as the ratio of the total heat transferred by the combined area of the fins, $${A_r},$$ and the exposed surface to that by the total area, $$A$$, if it were maintained at the base temp, $${T_0}.$$ Assuming uniform heat transfer coefficient over the entire surface, derive an expression for the relationship between efficiency and effectiveness of the fin.